# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Thursday, December 02, 2004, 12:15 pm

**Duration**: This information is not available in the database

**Location**: This information is not available in the database

**Speaker**: Georgios Mertzios (TU München)

## The Fixed-Parameter Cluster-Detecting Problem and applications

We handle here the complexity of the fixed-parameter cluster-detecting problem. This problem concerns the determination of a subgraph of a certain size and a certain constant density. The only known algorithm yet solves this problem in time *O(n*^{2c+4}), when applied to a graph on *n* nodes and *m* edges, where *c* is the fixed parameter of the problem. We present here two improved algorithms with complexity *O(n*^{2c+2}) and
*O(min{n*^{2c+2},nm^{2c+2}+n^{c+4}}) in worst case respectively. The second of these algorithms is essentially better for sparser graphs. The first one is also applied to the problem of measuring the design complexity, obtaining thus complexity *O(n*^{2c}) in worst case for that problem.

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